Solve for $p$, $ -\dfrac{3}{2p} = \dfrac{6}{p} - \dfrac{4p + 5}{p} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $2p$ $p$ and $p$ The common denominator is $2p$ The denominator of the first term is already $2p$ , so we don't need to change it. To get $2p$ in the denominator of the second term, multiply it by $\frac{2}{2}$ $ \dfrac{6}{p} \times \dfrac{2}{2} = \dfrac{12}{2p} $ To get $2p$ in the denominator of the third term, multiply it by $\frac{2}{2}$ $ -\dfrac{4p + 5}{p} \times \dfrac{2}{2} = -\dfrac{8p + 10}{2p} $ This give us: $ -\dfrac{3}{2p} = \dfrac{12}{2p} - \dfrac{8p + 10}{2p} $ If we multiply both sides of the equation by $2p$ , we get: $ -3 = 12 - 8p - 10$ $ -3 = -8p + 2$ $ -5 = -8p $ $ p = \dfrac{5}{8}$